Chip formation, acoustic emission and surface white layers in hard machining

Chip Formation, Acoustic Emission and Surface White Layers in Hard Machining J Barry I,G Byrne ( I ) , Department of Mechanical Engineering, University College Dublin, Ireland De Beers Industrial Diamonds Division, Ireland Abstract In hard machining, sawtooth chip formation is due to initiation of adiabatic shear within the lower region of the primary shear zone Catastrophic failure within the upper region of the shear zone occurs through either of two different mechanisms and results in the rapid release of elastic strain energy This periodic release of strain energy is the dominant source of acoustic emission during sawtooth chip formation In addition to adiabatic shearing in the primary and secondary shear zones, there is evidence to suggest that it occurs in the tertiary shear zone also; namely the surface white layer Keywords: Chip formation, Acoustic emission, Surface white layer INTRODUCTION The great utility of steels as engineering materials arises in part from the wide range of mechanical properties which may be obtained through the austenite-martensite (hardening) transformation and subsequent tempering processes The hardening operation involves heating the material to a sufficiently high temperature such that the lower temperature body centre cubic (BCC) a ferrite and cementite (Fe3C) phases transform to austenite, an interstitial solid solution of Carbon in face centred cubic (FCC) y Iron On rapidly cooling an austenitic steel to below its martensite-start temperature, the interstitial Carbon atoms are retained in solution despite the reverse transformation of the unit cell from FCC to a distorted body centred tetragonal (BCT) structure [I] The strains arising from the distortion of the unit cell result in either heavily dislocated or heavily twinned microstructures which in comparison to softer pearlite/ferrite structures of the same composition, are relatively unstable [2] When hard martensitic steels are deformed at sufficiently high strain rates, the plastic strain is accommodated in narrow localised adiabatic shear bands [3] It is shown below that it is this phenomena of adiabatic shear band formation which results in the formation of the sawtooth chip and the surface white layer in hard machining The influence of the chip formation mechanisms on acoustic emission (AE) is also discussed, for both sawtooth and continuous type chips EXPERIMENTAL Two grades of steel were employed in the current study; a BS817M40 steel, and a low alloy tool steel, similar to the AlSl L grades The composition of these steels are given in Table Both steels were oil quenched and tempered to various hardness levels, depending on the particular tests being undertaken The structure of both steels was lath martensite The low alloy tool steel also contained micron sized spheroidal alloy carbides Commercially available mixed ceramic cutting tools were used for most of the cutting tests This material contained Steel BS817M40 Tool steel C 0.40 0.80 Si 0.16 0.19 Cr 1.17 1.71 Ni 1.37 0.14 Mo 0.28 0.41 Table 1: The composition of the steels used for machining tests, in wt% 71% a-Al203, 28% TIC and 1% MgO and had an average grain size of pn The standard tool geometry was of IS0 (1832:1991) designation; TNGA 160412 T02020 The average edge radius, rp, was pn Table summarises the different cutting configurations employed in the study, the respective cutting conditions, work materials and hardness levels and tool materials and geometries The turning, facing, orthogonal and nonoverlapping cutting tests were undertaken using constant surface speed control on a CNC lathe equipped with a platform dynamometer Acoustic emission was measured with the sensor mounted on the underside of the tool holder To obtain the AERMSsignal, the raw signal was integrated with a time constant of TRMS = 12 ms The technique employed for quickstop testing is similar to that used by Betz [4] This orthogonal cutting technique involves setting the tool trajectory at a small angle (1 - 2') to the free surface of the workpiece such that there is a gradual increase in the cutting force with tool path Once the cutting force exceeds a critical value, the chip formation zone fractures from the body of the workpiece at a predefined (notched) location It is estimated that the deceleration of the tool is of the order of 5.106 m/s and that during the period of arrest, the tool travels no more than 4% of the undeformed chip thickness The nonoverlapping cutting technique developed during the course of this investigation is similar in principle to the planing arrangement used by Brinksmeier et al [5] in which the trajector of a round nosed tool is set at a very slight angle (0.006IY) to the flat surface of the workpiece Once the tool engages the workpiece, there is a gradual and continuous increase in both the depth of cut and the undeformed chip area In order to achieve higher cutting Cutting Configuration Turning & Facing Orthogonal Cuttina 2.94, 4.17 Quickstop 0.55, 1.42, 2.5, 4.7 Feed, t pn Depth of cut, ap, pn f = 100 pn ap = 200 pn f = 50, 100 pn Width of cut, b = mm h = - 100 (cont.) b=lmm Non-overlapping 1.67, 3.33 h, Cutting Speed, vc, m/s '67' 3'33' 5'0 I = - 100 (cont.) Work material & hardness (HRC) BS817M40, 52 Tool steel, 52, 58, 60 BS817M40, 52 Tool steel, 45, 51, 54, 59 BS817M40, 52 Tool steel, 45, 49, 56, 60 BS817M40, 39, 45, 48, 52, 54 Tool steel, 46, 51, 55, 60, 62 Tool material & geometry A120fliC, a = 6', y=-22', r E =1.2 mm A120fliC, a = 6' Y = -6' -22' -30' -40' W C/8 %CO, a=6',y=-22 A120fliC, a = 6', y=-22', r E =1.2 mm Table 2: The range of cutting conditions, work material hardness levels and tool materials and geometries for the different cutting tests undertaken (ha, denotes the maximum instantaneous undeformed chip thickness, see Figure 1) speeds in the current study, a nonoverlapping facing arrangement was employed in which the tool follows a spiral path with simultaneous feed in the axial direction Figure shows the manner in which the depth of cut, ap, the undeformed chip area, A and the engagement length, L, varies with tool path CHIP FORMATION MECHANISMS Hard steels are one class of materials from which sawtooth chips are produced, Figure (In addition to the hardness of the steel, higher cutting speeds and depths of cut favour the transition from continuous to sawtooth chip formation [6], [?'I) Since this chip form was first identified in the machining of Titanium alloys by Shaw in 1954 [8], many researchers have sought to understand its mechanism of formation 3.1 The Mechanisms of Sawtooth Chip Formation The quickstop tests undertaken in the present study offer clear insight into the underlying metallurgical instability responsible for sawtooth chip formation The optical micrograph in Figure shows a quickstop specimen produced from the low alloy tool steel of 56 HRC with a cutting speed of 85 m/min It is evident that cutting has been interrupted at a stage in the cyclic process when the incipient segment has undergone considerable upsetting (or compression deformation) Also, a thin white etching band is seen to extend from the tool tip partway along the primary shear zone That such a band did not form as a In brief, the different theories may be classified into those which propose the cyclic instability to be based on the initiation and propagation of cracks [7, 9, 10, 111, usually from the free surface of the workpiece, and those which are based on adiabatic shear initiation [6, 12, 131, a thermoplastic instability common in materials of limited strain hardening capacity when deformed at high strain rates and/or to large plastic strains [3] 0.01 1.o 0.08 mm 0.06 0.6 0.04 0.4 0) c C f Figure 2: Sawtooth (a) and continuous (b) chip types 0) 0.2 0.02 % C W 0 0.33 m 1.o Tool path, I, Figure 1: The variation in depth of cut, undeformed chip area (note cross section of undeformed chip area), and engagement length in nonoverlapping cutting tests While it may seem peculiar that such extremes in material behaviour can be both considered of relevance for the same process, it is worth noting that the crack theories of chip formation are usually qualified by the suggestion that subsequent sliding between the fracture surfaces results in the formation of the white etching bands which run along the underside of each 'tooth' in the chip Such white etching bands are also characteristic of localised adiabatic shear deformation and hence their presence indicates little of their mechanism of formation result of sliding friction across fracture surfaces, is evident from the fact that the cutting force at fracture is maximal (note the description of the quickstop technique in Section 2; see also reference [4]) If a crack had propagated down through the primary shear zone, a decrease in the cutting force would be expected Rather, this white band is a localised deformation band formed as a result of adiabatic shearing Based on the fact that its thickness is greater at the tool tip, it is assumed that shear localisation initiated there and propagated towards the tool tip The absence of shear localisation in the upper region of the primary shear indicates that the material there is deforming under strain hardening conditions While shear localisation contributes towards the destabilisation of the chip formation process, there is evidence to suggest that its occurrence does not guarantee failure within the primary shear zone Figure shows a quickstop specimen produced from the low alloy tool steel of 60 HRC with a cutting speed of 33 m/rnin Several distinct white shear bands are evident along the (left) tool side of the chip P I c - 20 prn Figure 3: Quickstop specimen obtained from the low alloy tool steel of 56 HRC with cutting speed, v, = 1.42 m/s Figure 5: Mechanisms of failure in the upper region of the primary shear zone; (a) ductile fracture, (b) large strain thermoplastic deformation (See text for details) Figure 4: Quickstop specimen obtained from the low alloy tool steel of 60 HRC with cutting speed, v, = 0.55 m/s The leftmost band, running along the edge of the specimen was formed within the secondary shear zone The remaining white bands were formed within the primary shear zone, however, it is clear that only for every second occurrence of shear localisation within the primary shear zone, was a discrete segment formed For the conditions under which the specimen in Figure was formed, it appears as though the decrease in shear stress within the lower region of the primary shear zone (where shear localisation occurs), was offset by an increase in shear stress within the upper region of the shear zone Under most cutting conditions, however, shear localisation within the lower region of the primary shear zone is sufficient to result in catastrophic failure over the whole of the shear zone Two mechanisms of failure have been observed within the upper region of the primary shear zone during sawtooth chip formation Under what may be described as severe cutting conditions, such as higher work material hardness and higher cutting speeds, ductile fracture occurs Figure 5(a) shows the underside of a chip segment produced in the orthogonal cutting of the low alloy tool steel of 60 HRC with cutting speed, v, = 3.3 m/s and feed, f = 100 pn The dimple structure is typical of ductile fracture in which voids nucleate, grow and coalesce [ I ] These dimple structures were evident only near the tip of the segment The underside of chip specimens produced from softer steels at lower cutting speeds not exhibit evidence of ductile fracture The specimen shown in Figure 5(b) reveals a structure which is similar to the finely spaced lamellae on the free surface of continuous chips This similarity suggests the mechanism of failure within the upper region of the primary shear zone during sawtooth chip formation (under moderate cutting conditions) is the same as is operative during continuous chip formation 3.2 Continuous Chip Formation It is known that continuous chips exhibit evidence of shear localisation on their free surface, albeit on a scale at least one order of magnitude less than that on sawtooth chips [14], [15] A more important distinction between the nature of the shear localisation on continuous and sawtooth chips is the relationship between the shear front spacings, D and d in Figure 2, and the undeformed chip thickness, h, On the free surface of continuous chips, the shear front spacing (equivalent to the lamella thickness) is largely independent of the undeformed chip thickness and is typically - pn For sawtooth chips, the shear front spacing is similar to the value of the undeformed chip thickness; generally within +/- 50% [12] Figure 6(a) shows the lamellae which characterise the free surface of most continuous chips; this particular chip was produced in the orthogonal cutting of the low alloy tool steel of 45 HRC with cutting speed, v, = 1.67 m/s and feed, f = 100 pn As the work material hardness and/or the values of cutting speed and undeformed chip thickness are increased, such that the onset of sawtooth chip formation is imminent, a transition in the structure of the free surface of the continuous chip occurs, from the lamellar structure, to what has been termed a 'fold'-type structure (This term is used as the structures are similar to the folds formed in loose fabric) Figure 6(b) shows the folds on the free surface of a continuous chip produced in the orthogonal cutting of the low alloy tool steel of 49 HRC with v, = 1.67 m/s and feed, f = 100 pn On comparison to the underside of the sawtooth chip shown in Figure 5(b), it is clear that the mechanisms of failure in the upper region of the primary shear zone are the same for both chip types Before discussing the mechanisms of fold formation, it is necessary to first consider the mechanisms of lamella formation When a lamellar-type continuous chip is sectioned, Figure 6(c), it is seen that the material has undergone fairly uniform shear strain as indicated by the reorientation of the fine martensite laths in a direction parallel to the shear stress (Note the random orientation of the martensite laths in the as-tempered work material (45 HRC), Figure 6(e)) It is reasonable to assume therefore, that lamellae form as a result of cleavage due to dislocation pileup and/or strain incompatibility at carbide or inclusion boundaries In contrast to this fracture mechanism, Ramalingam and Black [I61 and Black [14], [I71 proposed a localised thermal softening model in order to account for Lamella formation The validity of such a mechanism is not disputed, however, it is thought that in the machining of hardened steels, it more accurately describes the formation of folds Noting that the lamella to fold transition occurs with increases in work material hardness and/or increases in cutting speed and undeformed chip thickness, and that as each of these parameters is increased, thermal softening assumes a greater significance in the primary shear zone (as indicated by the eventual initiation of adiabatic shear), it is suggested that the formation of folds is due to very localised thermal softening which suppresses cleavage and the generation of new fracture surfaces Note, that in Figure 6(d), even though a void nucleated at the large carbide particle (in the right of the field), this does not appear to have resulted In cleavage The distinction between lamella and fold formation is illustrated in Figure 6(f) and 6(g) discussed below When sawtooth chips are produced, an additional source of AE is operative 4.1 AE During Sawtooth Chip Formation During the formation of a sawtooth chip, it is clear that the material ahead of the primary shear zone is periodically elastically strained; the instantaneous elastic strain energy being proportional to the integral of the product of the shear stress at the primary shear zone boundary and the elastic displacement of the shear zone boundary Within any given segment formation cycle, once shear localisation has destabilised the primary shear zone, failure occurs within the upper region of the primary shear zone, resulting in the release of the elastic strain energy As the frequency of segment formation is typically greater than 10 kHz, it is beyond the response of conventional dynamometers Using a thin film sensor sandwiched between the insert and the shim of the toolholder, Davies et al [I21 measured a periodic variation in the cutting force of the same frequency as segment formation, The release of strain energy is by far the dominant source of AE when sawtooth chips are produced This is best illustrated in the data from the nonoverlapping cutting tests, Figure Each of the five charts in Figure corresponds to a workpiece of a particular hardness The trace in each chart shows a median AERMSsignal as a function of depth of cut; the grey envelope indicates the level of scatter (all traces acquired lay within this envelope) The inset charts have a reduced vertical scale so as to more clearly show the data For each of these tests, the chip sample produced was examined in order to determine the approximate tool path after which the transition from continuous to sawtooth chip formation occurred For the low alloy tool steel with vc = 1.67 m/s, sawtooth chips were produced only from the workpieces of 59.6 and 61 HRC, at estimated depths of cut of 25 and 30 pn, respectively This clearly corresponds to the marked increases in AERMSat these points In comparison to the AERMS during continuous chip formation, which is between 0.05 - 0.1 V, the AERMS produced during sawtooth chip formation is at least one order of magnitude greater Figure 6: Lamellae (a) and ‘folds’ (b) on the free surface of continuous chips Sections through electroless Ni coated lamellar-type chip (c) and fold-type chip (e) As-tempered structure of the low alloy tool steel (45 HRC) Illustration of the mechanisms of lamella (f) and fold (9) formation, ACOUSTIC EMISSION AND CHIP MORPHOLOGY It is widely accepted that any physical phenomena which results in the rapid release of elastic strain energy is a potential source of acoustic emission (AE) Quantitative models of AE in metal cutting processes where continuous chips are produced, assume the energy of the signal to be proportional to the square root of the combined work rate of plastic deformation within the three shear zones (Figure 2) and the work rate of sliding friction over the rear of the tookhip contact length and on the flank wear land [18], [19] The validity of such ‘continuous chip’ AE models for the machining of hardened steels is Figure 7: AERMSversus depth of cut in the nonoverlapping cutting of the low alloy tool steel with cutting speed, vc = 1.67 m/s In each of the five charts, the depth of cut ranges from - 100 pn 4.2 AE During Continuous Chip Formation With regards to the sources of AE during continuous chip formation, the data in Figures 7(c - e) is insightful In each of these charts, the AERMSsignal is seen to increase rapidly once the tool engages the workpiece In Figure7(c), following this initial rapid increase, the AERMS signal increases at a much lower rate for the remainder of the cut In Figure 7(d), the AERMSsignal remains relatively constant following the initial increase while in Figure 7(e), the AERMSsignal actually decreases with increasing depth of cut before eventually levelling off Similar relationships were noted for the BS817M40 steel which allows for a nonproportional relationship between AERMSand the energy dissipated in the shear zones Noting that for each of the tests conducted, both the cutting force and the thrust force increased near-linearly with depth of cut, it is clear that the data in Figure 7(c - e) not obey many of the models developed to date for AE in metal cutting If as suggested in references [18], [I91 that the plastic deformation and/or friction are the dominant sources of AE in metal cutting, one would expect a monotonic increase in AERMSwith depth of cut Clearly, the increasing depth of cut results in an increase in the volume of material undergoing plastic deformation and an increase in the area of sliding friction It will be evident from the discussion on sawtooth chip formation that adiabatic shear localisation is an important metallurgical process when cutting hardened steels The characteristic features generated by adiabatic shearing are the distinctive white bands observed in the primary and secondary shear zones The surface white layer is another such localised shear band One phenomena which may partly account for the relationships evident in Figure 7(c - e) is that of lamella formation on the free surface of the chip Just as failure within the primary shear zone during sawtooth chip formation results in the rapid release of elastic strain energy, failure along the shear fronts between lamellae on continuous chips also results in the release of strain energy However, an important distinction here between the two chip types relates to the extent to which the localised failure propagates through the shear zone It was noted above that the average thickness of the lamellae on the free surface of continuous chips increases with undeformed chip thickness, up to a limiting value of 2-3 pn, beyond which the lamella thickness remains fairly constant, irrespective of depth of cut (see also reference [14]) This behaviour suggests that cleavage cracks or ‘shear fronts’ between lamellae not extend across the thickness of the chip to the tool rake face, for chips formed at depths of cut greater than approximately 10 pn Shaw’s model of plastic deformation in the primary shear zone [I51 is useful here; in particular the suggestion that the normal stress over the shear zone is maximal in the vicinity of the tool tip, monotonically decreasing to zero where the shear zone meets the free surface of the workpiece Near the free surface, cleavage cracks could initiate due to the lower normal stress there, whereas the propagation of such cracks towards the tool tip would be impeded by the increasing normal stress THE STRUCTURE OF SURFACE WHITE LAYERS Thin foil specimens of machined surfaces were prepared for transmission electron microscopy (TEM) examination such that the viewing direction was normal to the machined surface The specimens were thinned to electron transparency using a single jet electropolishing unit The machined face of each specimen was protected from attack using a methanol reservoir Specimens of surfaces machined with unworn and worn cutting tools, in addition to specimens of the as-tempered steels, were examined in a TEM using an acceleration voltage of 200 kV (Reference to a worn cutting tool indicates the tool was used for a period of time equal to the average tool life, T, For the BS817M40 steel, T, = 712s, VBC = 255 pm, for the low alloy tool steel, T, = 791s, VBC= 125 pn) The structure of the surfaces of both steels, machined with unworn and worn cutting tools, consisted of very fine, misoriented cells The cell size generally ranging from 10 - 100 nm, however, for the BS817M40 steel machined with a worn tool, a number of coarser cells, up to 250 nm, were observed Apart from ascertaining the cell size, no other microstructural features of the white layers could be resolved in transmission mode In electron diffraction mode, considerably more detail could be resolved Figure 8(a) shows an indexed selected area electron diffraction pattern from the as-tempered BS817M40 steel of 52 HRC The selecting area aperture was of pn projected diameter All diffraction patterns from both astempered steels were indexed as (cubic) martensite, a, and cementite, Figure 8(b) shows a diffraction pattern from a BS817M40 surface machined with an unworn cutting tool In this In the nonoverlapping cutting tests performed in this study, a round nose tool was used such that there was a continual variation in the undeformed chip thickness along the engagement length; ranging from (nominally) zero at the extremities of the engagement length to a maximum in the middle (see Figure 1) If the cleavage cracks, responsible for lamella formation, can only propagate a finite distance through the shear zone, towards the tool tip, it follows that only the cleavage cracks at the extremities of the engagement length can propagate as far as the tool rake face In the central region of the engagement length, where the undeformed chip thickness is greater, cleavage cracks would be rewelded due to the higher normal stress nearer the tool tip This theory may partly account for the relationships between AERMSand depth of cut during continuous chip formation It is suggested that cleavage during lamella formation is a significant source of AE and that only when the chip thickness is sufficiently small, the cleavage cracks extend to the tool face such that the elastic strain energy released contributes to the measured AE For thicker chips, it is thought that the elastic strain energy released during cleavage is absorbed within the primary shear zone While such a model cannot fully account for the trends in Figure 7(c - e), it does provide a mechanism Figure 8: Indexed diffraction patterns from an astempered BS817M40 steel (a) and BS817M40 surfaces machined with unworn (b) and worn (c) cutting tools particular pattern, martensite/ferrite, austenite and cementite reflections are present (Note, the continuous rings are composed of many thousands of discrete reflections; thus indicating a great number of reflecting cells) It is noted, however, that the austenite reflections are extremely faint and in a number of other patterns from surfaces machined with unworn cutting tools, austenite reflections were not present Also, in contrast to the discrete cementite reflections in the as-tempered steel, the cementite reflections from machined surfaces are in the form of faint continuous rings This indicates a great refinement in the size of the Iron carbide particles Figure 8(c) shows a diffraction pattern from a BS817M40 surface machined with a worn cutting tool As for the surface machined with an unworn tool, the pattern is composed of discontinuous rings, but is considerably spottier This indicates a much coarser cell structure Also, the austenite (y) reflections are quite intense and were noted in all patterns from surfaces machined with worn cutting tools This clearly attests to an increase in the volume of retained austenite with increased levels of tool wear, in agreement with the findings of Tonshoff et al [20] and Chou and Evans [21] In the low alloy tool steel specimens, similar observations were made; namely, an increase in the volume of austenite and a coarsening of the cell structure with increased levels of tool wear Note, the patterns in Figure 8(b) and 8(c) are typically of those obtained from adiabatic shear bands The increase in the volume of austenite in surfaces machined with worn cutting tools is thought to arise from the greater degree of completion of the reverse transformation in the incipient surface during machining In turn, this is most likely due to the increased energy input to the incipient surface and the correspondingly higher temperatures (Force measurements in orthogonal cutting tests indicate the average shear and normal stresses on the flank wear land to remain relatively constant, irrespective of wear land width, the respective values being, T~ = 400 MPa and os= GPa) CONCLUSIONS The instability resulting in sawtooth chip formation is adiabatic shear Prior to the onset of adiabatic shear, a finer scale thermoplastic deformation mechanism is evident This results in a transition in the free structure of the continuous chip, from the familiar lamellar structure to a 'fold'-type structure For both chip types, a dominant source of AE is the release of elastic strain energy, which in the case of the sawtooth chip, arises from failure across the primary shear zone, and in the case of the continuous chip, arises from the fine cleavage cracks which define the shear fronts between lamellae The surface white layer is a nanocrystalline layer of ferrite and austenite with extremely fine Iron carbides Both the austenite content and the cell size increase with increased levels of flank wear ACKNOWLEDGEMENTS This work was funded by Enterprise Ireland under their Basic Research Grants Scheme and was undertaken while Dr John Barry (co-author) was employed by the Mechanical Engineering Department, University College Dublin, Ireland REFERENCES [ I ] Reed-Hill, R.E., Abbaschian, R., 1992, Physical Metallurgy Principles, 3rdEd., PWS-KENT, Boston Hornbogen, E., 1983, Physical Metallurgy of Steels, in Physical Metallurgy, 3rd Ed., Cahn, R.W., Haasen , P., Eds., Elsevier Science, Holland Rogers, H.C., 1982, Adiabatic Shearing - 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415 [I81 Kannatey-Asibu, E, Dornfeld, D.A., 1981, Quantitative Relationship for Acoustic Emission from Orthogonal Cutting, ASME J Engng Ind., 103:330-340 [I91 Carolan, T.A., Kidd, S.R., Hand, D.P., Wilcox, S.J., Wilkinson, P., Barton, J.S., Jones, J.D.C., Reuben, R.L., 1997, Acoustic Emission Monitoring of Tool Wear During the Face Milling of Steels and Aluminium Alloys Using a Fibre Optic Sensor, Part 1: Energy Analysis, Proc IMechE, 21 1(B4):299-309 [20] Tonshoff, H.K., Brandt, D., Wobker, H.-G., 1995, Potential and Limitation of Hard Turning, SME Technical Paper, MR95 - 215 [21] Chou, Y.K., Evans, C.J., 1999, White Layers and Thermal Modelling of Hard Turned Surfaces, Int J Machine Tools & Manuf 39:1863-1881 I ... the Dynamics of Chip Formation in the Machining of Hard Metals, Ann CIRP, 46(1):25-30 [I31 Zhen-Bin, H., Komanduri, R, 1997, Modelling of Thermomechanical Instability in Machining, Int J Mech Sci.,... austenite in surfaces machined with worn cutting tools is thought to arise from the greater degree of completion of the reverse transformation in the incipient surface during machining In turn,... ‘continuous chip AE models for the machining of hardened steels is Figure 7: AERMSversus depth of cut in the nonoverlapping cutting of the low alloy tool steel with cutting speed, vc = 1.67 m/s In